Pythagorean Theorem Calculator

About the Pythagorean Theorem

The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (the side opposite the 90° angle) equals the sum of the squares of the other two sides: a² + b² = c². This fundamental relationship, known since ancient times, is one of the most important and widely used theorems in mathematics.

The theorem has hundreds of known proofs and appears in countless real-world applications. Construction workers use it to ensure walls are perpendicular (the 3-4-5 right triangle is a classic tool). Navigators use it to find distances. Computer graphics rely on it to calculate distances between pixels. GPS systems use extended versions for 3D distance calculations.

The converse is also true: if three sides a, b, c satisfy a² + b² = c², then the triangle is a right triangle. This lets you verify whether any triangle has a right angle without measuring the angle directly. Famous Pythagorean triples (integer solutions) include (3,4,5), (5,12,13), (8,15,17), and (7,24,25).